Periodic and quasi-periodic attractors for the spin-orbit evolution of Mercury with a realistic tidal torque

  title={Periodic and quasi-periodic attractors for the spin-orbit evolution of Mercury with a realistic tidal torque},
  author={Michele V. Bartuccelli and Jonathan H. B. Deane and Guido Gentile},
  journal={Monthly Notices of the Royal Astronomical Society},
In this paper, we make a detailed study of the spin-orbit dynamics of Mercury, as predicted by the realistic model which has been recently introduced in a series of papers mainly by Efroimsky and Makarov. We present numerical and analytical results concerning the nature of the librations of Mercury’s spin in the 3:2 resonance. The results provide evidence that the librations are quasi-periodic in time, consisting of a slow oscillation, with an amplitude of order of arcminutes, superimposed on… 

Spin-orbital Tidal Dynamics and Tidal Heating in the TRAPPIST-1 Multiplanet System

We perform numerical simulations of the TRAPPIST-1 system of seven exoplanets orbiting a nearby M dwarf, starting with a previously suggested stable configuration. The long-term stability of this

Fast numerics for the spin orbit equation with realistic tidal dissipation and constant eccentricity

We present an algorithm for the rapid numerical integration of a time-periodic ODE with a small dissipation term that is $$C^1$$C1 in the velocity. Such an ODE arises as a model of spin–orbit

Rotation and figure evolution in the creep tide theory: a new approach and application to Mercury

This paper deals with the rotation and figure evolution of a planet near the 3/2 spin–orbit resonance and the exploration of a new formulation of the creep tide theory (Folonier et al. in Celest Mech

Pseudo-synchronous solutions for dissipative non-autonomous systems

In the framework of KAM theory, the persistence of invariant tori in quasi-integrable systems is proved by assuming a non-resonance condition on the frequencies, such as the standard Diophantine

Rotation of a synchronous viscoelastic shell

Several natural satellites of the giant planets have shown evidence of a global internal ocean, coated by a thin, icy crust. This crust is probably viscoelastic, which would alter its rotational

Triaxial deformation and asynchronous rotation of rocky planets in the habitable zone of low-mass stars

Rocky planets orbiting M-dwarf stars in the habitable zone tend to be driven to synchronous rotation by tidal dissipation, potentially causing difficulties for maintaining a habitable climate on the




The dynamical evolution of terrestrial planets resembling Mercury in the vicinity of spin-orbit resonances is investigated using comprehensive harmonic expansions of the tidal torque taking into

Mercury's capture into the 3/2 spin-orbit resonance as a result of its chaotic dynamics

It is shown that the chaotic evolution of Mercury's orbit can drive its eccentricity beyond 0.325 during the planet's history, which very efficiently leads to its capture into the 3/2 resonance.

Spin–orbit evolution of Mercury revisited

The theory of secondary resonances in the spin–orbit problem

We study the resonant dynamics in a simple one degree of freedom, time dependent Hamiltonian model describing spin-orbit interactions. The equations of motion admit periodic solutions associated with


We investigate the spin-orbital evolution of the potentially habitable super-Earth GJ 667Cc in the multiple system of at least two exoplanets orbiting a nearby M dwarf. The published radial

Tidal synchronization of close-in satellites and exoplanets. III. Tidal dissipation revisited and application to Enceladus

This paper deals with a new formulation of the creep tide theory (Ferraz-Mello in Celest Mech Dyn Astron 116:109, 2013—Paper I) and with the tidal dissipation predicted by the theory in the case of

The high-order Euler method and the spin–orbit model.

An algorithm for the rapid numerical integration of smooth, time-periodic differential equations with small nonlinearity, particularly suited to problems with small dissipation, is presented and implemented in standard double precision arithmetic.

Tidal synchronization of close-in satellites and exoplanets: II. Spin dynamics and extension to Mercury and exoplanet host stars

This paper deals with the application of the creep tide theory (Ferraz-Mello, Celest Mech Dyn Astron 116:109, 2013a) to the rotation of close-in satellites, Mercury, close-in exoplanets, and their